The Vacuum Cannon

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The Vacuum Cannon

• A Penetrating View Into the Physics of Pressure,
  Force, and Acceleration

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Pressure, Force, and Area

• Pressure is defined by the equation
• P pressure
• P F F force
• A A area
• The SI units for pressure are Pascals

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Pressure, Force, and Area

• Atmospheric Pressure is
• Force vs. Pressure

101.3kPa101300N/m2
- Force is given by Newtons 2nd Law Fma
- Force tells you how an object will accelerate
- Pressure tells you how an object will feel a
Force
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Example 1

• Shaquille ONeal has a mass of 150kg and wears
  size 22 shoes, which have an area of
  approximately 1000cm2 each. A female with a mass
  of 60kg wears stilettos with an area of 1cm2 on
  each heel and 24 cm2 on each toe. Calculate the
  pressure exerted by each person on the ground.
  Which Shoe would you rather have step on your
  foot?

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Example 1Cont (Shaqs Basketball Shoe)
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Example 1Cont (High Heels)
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Example 1Cont

• So who would you rather have step on your foot?
• Shaqs Basketball Shoe P7350Pa
• High Heel P117600Pa

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Atmospheric Pressure How Much is it Really?

• Atmospheric Pressure is measured as 101300N/m2.
  Remember what pressure a 60kg woman in high heels
  applied when stepping on 25cm2 of you, it was
  117600N/m2. This means that atmospheric pressure
  is similar to a 60kg woman standing in high heels
  on every 25cm2 of your body.

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Now Lets Take a Look at an Application The
Ping-Pong Ball Vacuum Cannon
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A Very Important Piece
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The First Thought
What does Newtons Second Law tell us?
How can we relate Pressure, Force and, Area?
What does this give us for Acceleration under
constant pressure?
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Lets Do Some Math

• What muzzle velocity do these equations give us?

• Is this reasonable?

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Lets Correct This

• As the ping-pong ball moves along the cannon the
  air entering not only accelerates the ping-pong
  ball but the growing column of air behind it.1
  This gives us a new equation for velocity.

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This gives us a corrected v(x1.5m)241.8m/s
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Lets Look at this Graphically
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How Pressure is Measured
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A Few Fun Facts from Researchers

• The Ek can be higher than that of a .22 caliber
  handgun.2
• If He-gas is used to accelerate the ball instead
  of air velocities as high as 370m/s have been
  recorded. 3

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Now Who Wants to See it in Action?
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Citations

• American Journal of Physics, Vol. 72, No. 7, pp.
  961963, July 2004
• The ballistics of many guns can be found at
  http//www.volny.cz/buchtik/Revo/Ballistic_Info_ko
  mplet.htm
• The Physics Teacher, Vol. 43, No. 1, pp. 2225,
  January 2005